Atlas1,811 of 3,942

II.C.51

m₃ = 0.75

From Li & Liao (2017)

II.C.51 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 64.002 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 11.07), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00312 of each other at a top speed of 19.1, line up 86 times a period, and the computed loop closes to 1.9×10⁻²⁶.

Measured over one period

Period: 64.00157521
Masses: 1 : 1 : 0.75
Energy: -1.33515
Angular momentum: 0
Closest approach: 0.003120
Top speed: 19.08
Path length: 164.98
Alignments per period: 86
Topology: abaBabaBAbaBAbabAbabABabABabaBabaBAbaBAbabAbabABabABabAB (free-group class)
Stability: unstable (|λ|max 11.07)
Loop closure: 1.9×10⁻²⁶

Neighbours on the map

All II.C orbits, the families of periodic three-body orbits, or the atlas map.